Rubbery flow

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

Knoff,W.F., Hopkins,I.L., Tobolsky,A.V. Studies on the stress relaxation of polystyrenes in the rubbery flow region. II. Macromolecules 4,750-754 (1971). 

Figures 1 to 3 also show that the decrease from the rubbery plateau to the rubbery flow is more rapid for plasticized PVC than for the pure polymer. This has been previously observed for polystyrene and plasticized polystyrene (27). Maximum relaxation times have been shown to be shorter for the plasticized sample due to the decrease in T0 as well as to a decrease in apparent average molecular weight (27). A similar interpretation applies in the case of plasticized polyviny. chloride.

Oefor -motion Hookian Glassy Secondary transition Primary transition Highly elastic rubbery Flow... 

Mechanical Behaviour Glassy Leathery Rubbery- elastic Rubbery flow Liquid flow... 

The rubbery plateau can be "stabilised" by cross-linking, the regions of rubbery flow and liquid flow are completely suppressed if enough chemical cross-links are introduced to serve as permanent network junctions in place of the temporary chain entanglements. Crystallisation is a kind of physical cross-linking with (numerically) many junctions. It is understandable that the amorphous state is more or less "stabilised" by crystallisation, so that the transition becomes less pronounced. 

Figure 3-23. Comparison of the relaxation behavior of the empirical KWW expression of equation (3-104) with data for PIB in the rubbery flow region. Data NBS PIB see Ferry1 for a table of these data. Copies of the data are also in the CD (PIB-Rel-1. TXT and PIB-Rel-2. TXT).

Figure 4-8. Simulations of master curves and modulus vs. temperature curves for a glassy polymer, (a) The master curves, shown at increments of 5 °C tend to be spaced more widely as the temperature is lowered because of the nature of the WLF relationship used for the temperature dependence [see Figure (4-6)]. (b) Demonstration of the influence of measurement time on the shape of the modulus-temperature curve. As the measurement time increases (by 1-decade increments), the apparent Tg decreases but the sharpness of the transition increases. (Simulation uses Smith empiricism8 for glass transition and the KWW function for the rubbery flow region.)...

Rubbery flow After the rubbery plateau the modulus again decreases from lO to 10 Nm in the section D to E. The effect of applied stress to a polymer in states (3) and (5) is shown in Figure 13.1(c), where there is instantaneous elastic response followed by a region of flow. 

At still higher temperatures, the rubbery flow and liquid flow regions are encountered, regions 4 and 5. In the former, flow is hindered by physical entanglements. At higher temperatures molecular motion is sufficiently rapid that molecules behave more nearly independently. 

Molecular flow, which occurs in the rubbery flow and liquid flow regions (regions 4 and 5 in Figure 1.12). 

As shown in Fig. G.2, the temperature at which the polymer behavior changes from glassy to leathery is known as the Tg. The rubbery plateau has a relatively stable modulus until, as the temperature is further increased, a rubbery flow begins. Motion at this point does not involve entire molecules, but in this region deformations begin to become nonrecoverable as permanent set takes place. As temperature is further increased, eventually the onset of liquid flow takes place. There is little elastic recovery in this region, and the flow involves entire molecules slipping past each other. 

DMA methods are widely used by thermal analysts to determine the viscoelastic properties of pol5uners for a number of purposes (see Viscoelasticity). The primary application of these techniques to the study of polymeric solids and melts is well documented. Excellent general discussions covering the subject are provided in References 70-72. Linear Amorphous Polymers (qv) exist in a number of characteristic physical states depending on the time scale and temperature of measurement. These are illustrated in Figure 31 in terms of an arbitrary modulus fimction and are classified as glassy, leathery, rubbery, rubbery flow, and viscous (73). All linear amorphous polymers exhibit these five physical states when they... 

Rubbery flow The motion of polymer molecules as a whole becomes important. Now major configurational changes take place on the order of 10 s. 

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